Quasi-periodic Waves and Solitary Waves to a Generalized KdV-Caudrey-Dodd-Gibbon Equation from Fluid Dynamics

In this paper, a generalized KdV-Caudrey-Dodd-Gibbon (KdV-CDG) equation is investigated, which describes certain situations in the fluid mechanics, ocean dynamics and plasma physics. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study its Hirota’s bilinear...

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Published inTaiwanese journal of mathematics Vol. 20; no. 4; pp. 823 - 848
Main Authors Tu, Jian-Min, Tian, Shou-Fu, Xu, Mei-Juan, Zhang, Tian-Tian
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.08.2016
Subjects
Mathematical functions
Mathematical procedures
Nonlinear equations
Polynomials
Solitons
Waves
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ISSN1027-5487
2224-6851
DOI10.11650/tjm.20.2016.6850

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Summary:In this paper, a generalized KdV-Caudrey-Dodd-Gibbon (KdV-CDG) equation is investigated, which describes certain situations in the fluid mechanics, ocean dynamics and plasma physics. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study its Hirota’s bilinear form andN-soliton solution, respectively. Furthermore, based on the Riemann theta function, the one-quasi- and two-quasi-periodic wave solutions are also constructed. Finally, an asymptotic relation of the quasi-periodic wave solutions are strictly analyzed to reveal the relations between quasi-periodic wave solutions and soliton solutions. 2010Mathematics Subject Classification. 35Q51, 35Q53, 35C99, 68W30, 74J35. Key words and phrases. Generalized KdV-Caudrey-Dodd-Gibbon equation, Hirota’s bilinear method, Riemann theta function, Soliton wave solution, Quasi-periodic wave solution.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.20.2016.6850